Simplify (x^-1-y^-1)/((xy)^-1)

$\frac{x^{- 1} - y^{- 1}}{{(x y)}^{- 1}}$

Move ${(x y)}^{- 1}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$(x^{- 1} - y^{- 1}) (x y)$

Simplify each term.

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$(\frac{1}{x} - y^{- 1}) (x y)$

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$(\frac{1}{x} - \frac{1}{y}) (x y)$

To write $\frac{1}{x}$ as a fraction with a common denominator, multiply by $\frac{y}{y}$ .

$(\frac{1}{x} \cdot \frac{y}{y} - \frac{1}{y}) (x y)$

To write $- \frac{1}{y}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$(\frac{1}{x} \cdot \frac{y}{y} - \frac{1}{y} \cdot \frac{x}{x}) (x y)$

Write each expression with a common denominator of $x y$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{x}$ by $\frac{y}{y}$ .

$(\frac{y}{x y} - \frac{1}{y} \cdot \frac{x}{x}) (x y)$

Multiply $\frac{1}{y}$ by $\frac{x}{x}$ .

$(\frac{y}{x y} - \frac{x}{y x}) (x y)$

Reorder the factors of $y x$ .

$(\frac{y}{x y} - \frac{x}{x y}) (x y)$

Combine the numerators over the common denominator.

$\frac{y - x}{x y} (x y)$

Cancel the common factor of $x y$ .

Cancel the common factor.

$\frac{y - x}{x y} (x y)$

Rewrite the expression.

$y - x$